GSC OU is my favorite OU tier and I was quite sad to see GSC 1v1 is both entirely abandoned and uninteresting. I think to anyone who understands GSC mechanics understand why GSC 1v1 might have some issues. I plan to work on amending those issues, but first I'll explain the three things that are problematic.
#1: Sleep Moves and Sleep Talk
While Sleep moves were banned from the previous incarnation of GSC 1v1 and I don't think they belong back. Jynx basically kills anything under 95 speed and Persian while relying on Hypnosis does basically the same thing albeit less reliably, overall just introduces an unnecessarily luck based factor into the tier especially when considering OHKO'g things in GSC is nigh-impossible (I'll get to that later.)
I think the main issue at hand would be Sleep Talk. In GSC, Sleep Talk can call Rest and both get you back to full HP and reset the Rest counter. This makes reliably killing things a massive pain in the neck when considering any chip may be undone at a moment's notice and as stated earlier introduces RNG into the tier. I don't think the solution would be banning Rest as than you have the massive issue of Toxic/TWave becoming incredibly busted. Banning Sleep Talk would kill the RNG factor and make reliably setting up on asleep pokemon more reliable. How you go about solving Rest as a move is tricky because if you ban Rest Toxic runs amok. A Rest ban
could work since offensive mons don't care and some stall mons have Heal Bell anyways to keep Toxic in check, but this doesn't fix TWave being incredibly annoying. I would like to hear more thoughts on this.
#2: Berserk Gene
I think this is a pretty cut and dry case of an item that simply doesn't belong in 1v1. Berserk Gene basically applies Swagger to the mon that holds it when sent out. Either leads to a mon being able to get way too strong for no drawback or killing on mon based on bad confusion pulls. I think beforehand it was kept unbanned as a necessary evil, being able to provide mons w/ breaking capabilities since choice items don't exist. In my opinion I don't think this solves the issue as opposed to creating a new one. Basically forces people to use breakers that may just kill themselves (keep in mind Confusion is 50% this gen) or Marowak. Not a healthy presence in the tier both parts of the item are inherently ridiculous don't see much reason to keep it in the tier.
#3: EVs/DVs and Lack of Natures
I think this is the largest hurdle GSC 1v1 faces. Every EV is maxed out from the get-go meaning everything is insanely bulky and strong. However, it is important to note
strength does not scale up with bulk. This is due to a lack of offensive items such as LO or choice items in addition to the fact that there aren't any boosting natures. Overall, mons are just fatter than they are strong. This leads to stall sets likely to dominate especially when you consider the lack of anti-stall options such as Trick or Taunt. There is no way to get around this w/o some kind of modification that limits EVs to 508 (as per usual) but you're being unfaithful to GSC at that point. The focus should be shifted to balancing things around this instead of trying to fix it through modification, wanted to make this section to highlight how important this is to GSC.
So where do we go from here? The answer is bans!
Snorlax and the combo of Encore+Disable should be banned!

Snorlax is a nigh unkillable beast. Boasting monstrous 160/65/110 bulk and Normal typing it becomes insanely rough to break especially when you consider its massive movepool. Counter and Curse making poking at its lower defense difficult and its serviceable special coverage in Fire Blast, Ice Beam, and TBolt make it quite insane especially when you can run special moves at no cost outside of a moveslot. You also have to keep in mind that options for Fighting STAB are incredibly limited w/ the best options being HP Fighting and Cross Chop. Overall Lax would just be a massive hassle in the builder and on preview, Lax is generally busted in 1v1 shouldn't be a shock that in the gen Lax the best mon in OU that it wouldn't be a fit for 1v1.

Encore lasts from 3-7 turns in GSC and Disable 1-7. Even considering the 55% accuracy Disable has this seems incredibly annoying. I'm down for testing Dewgong since it has its fair share of issues but Alakazam w/ Encore/Disable/Recover/Barrier seems highkey unbeatable. Not a fan of a mechanic that basically forces your check to be "get lucky." EDIT: Struggle only doing 1/4 of the damage dealt may mean this is fine but I'm still of the opinion this should be looked at
I do hope that GSC can develop in some capacity. If you are interested in developing or playing the tier DM me at zioziotrip#4846 on Discord.